Paid by whom?
Who pays men for their role in raising children? Some men are primary parents, and increasingly so.
Who pays men for their role in raising children? Some men are primary parents, and increasingly so.
theoretically some women could pay some quality fathers for coparenting , but it would be rare.
It sounds like your idea is that women get paid to have the joys of being a parent, while men pay to get nothing in return.
If the woman and children do live with the man then essentially you are recreating the idea of a male provider married to a housewife, except more transactional and unequal.